It reminds me also of people who swear by using default settings in their editor or other programs so they can feel at home anywhere. Yeah, that's sort of a benefit, but I don't think it outweighs optimizing your workflow at your own machine.
I had a friend who used a split keyboard, blank keycaps, and a very odd layout (QGMLWB or BEAKL2 I think) at work. IIRC he said he kept a second normal keyboard at his desk for when someone would come by to pair program. This is sorta the inverse of your scenario. I guess he'd need to carry his keyboard to someone else's desk, or just type slower.
Back in the in-person days when sharing a keyboard with a coworker was more common, you have the very handy switcher icon in the taskbar.
So what you say counts for any non-standard keyboard. There's always a learning curve. I tried going to 60%, now I settled for 80%/TKL and there are situations where I miss the other 20%, but my (vertical) mouse is in a more natural position. At least with Dvorak, all the physical keys are the same size as a standard Qwerty, so you could just set to Qwerty English-American and be done with it.
In this normal scenario, the keyboard layouts do not matter.
"Tech support" when both people are in the front of the same computer happens more between friends or colleagues, when typing speed does not matter, than in professional corporate tech support.